Arithmetic Reasoning

4. A duplicator can make 75 copies of a letter per minute, and 300 copies from one master. After how long must the master sheet be changed?

a. 4 minutes

b. 5 minutes

C. 6 minutes

d. 15 minutes

Answer:

(1,–1), (4, –2), (9, –3)

Step-by-step explanation:

In the picture attached, the plot of the function f(x) = -√x is shown.

To verify which points lie on the line we compute the following table.

x    √x    f(x) = -√x

1     1        -1

4    2       -2

9    3       -3

The points which lie on the graph will be (1,–1), (4, –2), and (9, –3) so the correct answer is option D.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the picture attached, the plot of the function f(x) = -√x is shown. To verify which points lie on the line we compute the following table.

x    √x    f(x) = -√x

1     1        -1

4    2       -2

9    3       -3

We can see that the above points are satisfying the function. Therefore points that lie on the graph will be (1,–1), (4, –2), and (9, –3) so the correct answer is option D.

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Answer:

9.110° and y are the same(alternate angles)

thus y=110°. 110+x=180(seplementary angles). thus x=180-110=70°

z(alternate)=70°

10.y=78°. x=(180-78)=102°. z=102°

11.x=83°. y=(180-83)=97°. z=97°

12.y=37°. x=(180-37)=143. z=143°

to confirm the answers all angles in a circle at the centre add up to 360°

Answer: 63 square units

Step-by-step explanation:

Area of a parellelogram = b x h

7 x 9 = 63 square units

Answer:

63

The triangle can be moved to the other side making the parallelogram a rectangle with a length and width of 7 and 9

7 x 9 = 63

Step-by-step explanation:

Answer:

40cm^2

Step-by-step explanation:

A=a+b/2×h

A=6+10/2*5

A=16cm/2*5cm

A=8cm*5cm

A=40cm^2

Answer:

4th option is the correct answer

35 inches

Step-by-step Explanation:

[tex]w = 4 \frac{3}{8} = \frac{35}{8} \: in \\ \\ l = 3 \times \frac{35}{8} = \frac{105}{8} \: in \\ \\ perimeter \: of \: rectangle \\ = 2\bigg(l + w \bigg) \\ \\ = 2\bigg( \frac{105}{8}+ \frac{35}{8} \bigg) \\ \\ = 2 \times \frac{140}{8} \\ \\ = \frac{140}{4} \\ \\perimeter \: of \: rectangle = 35 \: in[/tex]

Answer:

[tex]26.14yd^2[/tex]

Step-by-step explanation:

Triangle

[tex]A=\frac{h_bb}{2} \\=\frac{4*6}{2} \\=12yd^2\\\\A=\frac{1}{2} \pi r^2\\=\frac{1}{2} \pi 3^2\\=14.14yd^2\\\\12+14.14=26.14yd^2[/tex]

Answer:

Step-by-step explanation:

The area of a circle knowing the diameter is 28.2743, now divide between 2: 14,13715

Now the area of the triangle give us: 9.238

9.238 + 14,13715 = 23.37515

The procedure is in the images

App used: CalculateMyFigure

Answer:

t = 5 sec

Step-by-step explanation:

h = - 16t² + 32t + 240

On the ground h = 0.

- 16t² + 32t + 240 = 0 / : (- 16)

t² - 2t - 15 = 0

(t-5)(t+3) = 0

t = 5, t = - 3

Time can be only positive, so t = 5 sec

Answer:

A

Step-by-step explanation:

[tex]\sqrt{(-5 - (-1))^{2} + (7 - 2)^{2} } = \sqrt{41}[/tex]

So the right answer is √41

please see the attached picture for full solution

Hope this helps

Answer:

1. 4

2. -4

3. -4

Step-by-step explanation:

Let's look carefully at each problem and explain it.

1. (-2)^2

This means find the square of the number -2. Since the square of a number means multiplying the number by itself, then

(-2)^2 means the product (-2) * (-2),

and since the product of two negative numbers is positive, then

(-2)^2 = (-2) * (-2) = 4

Answer is 4.

2. -2^2

Here, the exponent applies only to the 2, not to -2. This problem means square 2 and then take the opposite of the product. This can be written as

-(2^2)

-2^2 = -(2^2) = -(2 * 2) = -(4) = -4

Answer is -4.

3. -(2)^2

This is the same as problem 2 above. You square the 2 first, then take its negative.

-(2)^2 = -(2^2) = -(2 * 2) = -(4) = -4

Answer is -4

Answer:

15 minutes more, as 60-45mins = 15 minutes

Step-by-step explanation:hope it helps

It will take 15 more minutes for the journey than the expected.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

The distance from Raj's house to the airport is 30 miles.

He expects the taxi to travel at an average speed of 40 mph.

If he travels at a speed of 40 mph, let t be the time taken.

Speed = Distance / Time

40 = 30 / t

t =  = 0.75 hours = 45 minutes

If Raj's taxi actually travels at an average speed of 30 mph, let t' be the time taken.

30 = 30 / t'

t' = 1 hour = 60 minutes.

t' - t = 60 - 45 = 15 minutes

Hence the journey takes 15 more minutes than expected.

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Answer:

a)   45

The sequence  3 , 5, 9 , 15 , 23 , 33 , 45

Step-by-step explanation:

Given The sequence  3 , 5, 9 , 15 , 23 , 33

First term = 3

Add 2  of first term  

Second term  = 3 +2 = 5

Add 4  of second term  

Third term = 5 + 4 = 9

Add 6  of Third term  

Fourth term  = 9 + 6 = 15

Add 8 of  fourth term

fifth term = 15 + 8 = 23

Add 10 of fifth term

sixth term = 23 + 10 = 33

Add 12 of sixth term

seventh term = 33 +12 = 45

Final answer:-

Now the sequence   3​, 5​, 9​, 15​, 23​, 33​, ​__45___

Answer:

The Surface Area = 2 B + p h. So True

Step-by-step explanation:

Answer: y=-(3x-2)= -3x+2

The intercept with y is 2

The intercept with x is 2/3

Answer:

1764 ways

Step-by-step explanation:

Given:

Men = 9

Women = 7

Required Men: 3

Required Women: 2

'

Required

Total Possible Outcome

The total possible outcome can be determine as follows;

Total = (Selection of Men) and (Selection of Women)

Calculating Selection of Men;

Let n represent total number of men; This implies that n = 9;

Let r represent number of men to select; This implies that r = 3;

The selection can be done in the following ways;

[tex]Male = nCr[/tex]

Where [tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

[tex]Male = 9C3[/tex]

[tex]Male = \frac{9!}{3!(9-3)!}[/tex]

[tex]Male = \frac{9!}{3!(6)!}[/tex]

[tex]Male = \frac{9 * 8 * 7 * 6!}{3!6!}[/tex]

[tex]Male = \frac{9 * 8 * 7}{3!}[/tex]

[tex]Male = \frac{9 * 8 * 7}{3*2*1}[/tex]

[tex]Male = 84 ways[/tex]

Calculating Selection of Women;

Let n represent total number of men; This implies that n = 7;

Let r represent number of men to select; This implies that r = 2;

The selection can be done in the following ways;

[tex]Female = nCr[/tex]

Where [tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

[tex]Female = 7C2[/tex]

[tex]Female = \frac{7!}{2!(7-2)!}}[/tex]

[tex]Female = \frac{7!}{2!(5)!}[/tex]

[tex]Female = \frac{7 * 6 * 5!}{2!5!}[/tex]

[tex]Female = \frac{7 * 6}{2!}[/tex]

[tex]Female = \frac{42}{2*1}[/tex]

[tex]Female = 21 ways[/tex]

Recall that

Total = (Selection of Men) and (Selection of Women)

Hence,

[tex]Total = 84 * 21[/tex]

[tex]Total = 1764 ways[/tex]

Answer:

1

Step-by-step explanation:

-3a+4 =7

-4. _4

-3a=3

divide by -3 on both sides

a=-1

3+4=7

Answer:

a= [tex]-3\frac{2}{3}[/tex] or ≈ -3.66

Step-by-step explanation:

-(3a+4)=7

-3a-4=7

Add 4 to both sides

-3a=11

Multiply both sides by -1

3a= -11

Divide both sides by 3

a= [tex]-3\frac{2}{3}[/tex]

Answer:

g(5)=17

Step-by-step explanation:

g(x)=3x+2

Let x = 5

g(5) = 3*5+2

      = 15+2

      = 17

Answer:

17

Step-by-step explanation:

Just substitute 5 into the position of X

Answer:

3/10

Step-by-step explanation:

Answer:

50%

is the probability of this question

Answer:

25%

Step-by-step explanation:

We have 4 choices when flipping two coins, HH, HT, TH and TT where H and T are heads and tails respectively. The only option where both coins will not land on heads is TT so the probability is 1/4 = 25%.

Answer:

(2,5)

Step-by-step explanation:

Choose values for  x  and substitute in to find the corresponding  y  values.

(2) - 2y = -8

2 = 2y - 8

10 = 2y

5 = y

(2,5)

Answer:

Step-by-step explanation:

DB=√(y²-25)

again DB=√(x²-36)

so √(y²-25)=√(x²-36)

squaring

y²-25=x²-36

x²=y²-25+36

or x²=y²+11

also x²+y²=(6+5)²

x²+y²=121

y²+11+y²=121

2y²=121-11

2y²=110

y²=110/2=55

y=√55

Answer:

x=27

Step-by-step explanation:

So let's look at the ratio

3:9

x:81

x is proportional to 3 the same way that 81 is to 9

How would we get 9 to 81?

We would multiply by 9

So what is 3*9?

27

Answer:

[tex]3[/tex]

Step-by-step explanation:

[tex]2x-18=-2y+12[/tex]

[tex]y=12[/tex]

[tex]2x-18=-2(12)+12[/tex]

[tex]2x-18=-24+12[/tex]

[tex]2x-18=-12[/tex]

[tex]2x-18+18=-12+18[/tex]

[tex]2x=6[/tex]

[tex]\frac{2x}{2} =\frac{6}{2}[/tex]

[tex]x=3[/tex]

Answer:

x = 3

Step-by-step explanation:

=> 2x-18 = -2y+12

Given that y = 12

Putting in the above equation to get the value of x

=> 2x-18 = -2(12)+12

=> 2x-18 = -24+12

=> 2x-18 = -12

Adding 18 to both sides

=> 2x = -12+18

=> 2x = 6

Dividing both sides by 2

=> x = 3

Answer:

Step-by-step explanation:

this is a radical equation:

when x=1 y=0

reflected about x

-sqrt(x)

right 1 unit

-sqrt(x-1)

it looks like y-int is about (0,1/3)

vertically compressed by a factor of 1/3

-(1/3)sqrt(x-1)

if you think the y-int is more (0,1/4), then

the function is vertically compressed by a factor of 1/4

-0.25sqrt(x-1)

Answer:

1.785 cm / min

Step-by-step explanation:

We have to the following equation:

V = A * L

The volume is equal to the area times the length, now, if we derive with respect to time we have:

dV / dt = dA / dt * L

Now, the area of a trapezoid is:

A = (Upper base + Lower base) / 2 * height

Now we have:

Upper base = 40 + h

Lower base = 40

Replacing we have:

A = (40 + h + 40) / 2 * h

A = (h ^ 2) / 2 + 40 * h

Now, we derive and we are left:

dA / dt = d [(h ^ 2) / 2 + 40 * h] / dh * dh / dt

dA / dt = (h + 40) * dh / dt

we replace dA / dt:

dV / dt = [(h + 40) * dh / dt] * L

We have that dV / dt is equal to 0.1 m ^ 3 / min, we know that 1m ^ 3 is equal to 10 ^ 6 cm ^ 3, therefore:

dV / dt = 10 ^ 5 cm ^ 3 / min

in addition L is equal to 8 m or what is equal to 800 cm, and also h at the required moment is 30 cm

we replace everything and we have:

10 ^ 5 = 800 * (30 +40) * dh / dt

dh / dt = 10 ^ 5/56000

dh / dt = 1.785 cm / min

Answer: 3.3%

Step-by-step explanation:

Amount = prt / 100

3075.21 = (2152 x r x 13)/100

Answer:

the answer is letter c

Step-by-step explanation:

Answer:

250 dimes

Step-by-step explanation: